Optimal Controlled Nodes Selection for Fast Consensus

Motivated by the significance of optimizing network performance with limited resources in real applications, we investigate the problem of achieving fast and desired consensus in a complex network via pinning control a fraction of nodes in the network. An optimization problem is proposed to select p optimal pinned nodes to guarantee fastest consensus, which is relaxed to a Mixed‐Integer Semi‐Definite Program. In the single pinned node case ( i.e. , p = 1), we find that the optimal pinned node is the node with highest min‐max distance centrality within the nodes with highest closeness centrality in the network. In the multiple pinned nodes case ( i.e. , p > 1), we find that betweenness centrality could be used as a suboptimal index to select pinned nodes.